Let a₁, a₂, ..., a₃ₙ be an arithmetic progression with a₁ = 3 and a₂ = 7. If a₁ + a₂ + ... + a₃ₙ = 1830, then what is the smallest positive integer m such that m(a₁ + a₂ + ... + aₙ) > 1830?

If f(x) = (5x + 2)/(3x − 5) and g(x) = x² − 2x − 1, then the value of g(f(f(3))) is :

In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?

If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is :

The shortest distance of the point (1/2, 1) from the curve y = |x − 1| + |x + 1| is

Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?

If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a − b)² + (a − c)² + (a − d)² is

If f1(x) = x² + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is :

For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied?